document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202853>Question 1202853</A>: <I><SPAN STYLE=\"word-break: break-all;\"> -6x+3y=-9 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838032 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=838032\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Solving for y.<BR>\n" );
document.write( "-6x+3y = -9<BR>\n" );
document.write( "3y = -9+6x<BR>\n" );
document.write( "3y = 6x-9<BR>\n" );
document.write( "y = (6x-9)/3<BR>\n" );
document.write( "y = (6x)/3-(9/3)<BR>\n" );
document.write( "y = 2x-3<BR>\n" );
document.write( "A tool like GeoGebra's CAS feature, or WolframAlpha, can be used to verify the answer.\r<BR>\n" );
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document.write( "Let's find a few points on this line.<BR>\n" );
document.write( "To do so, we plug in values for x to get a paired value for y. <BR>\n" );
document.write( "This will give us the (x,y) points needed.\r<BR>\n" );
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document.write( "For example, plug in x = 0.<BR>\n" );
document.write( "y = 2x-3<BR>\n" );
document.write( "y = 2*0-3<BR>\n" );
document.write( "y = 0-3<BR>\n" );
document.write( "y = -3<BR>\n" );
document.write( "The input x = 0 gives the output y = -3.<BR>\n" );
document.write( "The point (0,-3) is on the line.<BR>\n" );
document.write( "A shortcut is to compare y = 2x-3 to y = mx+b to find that b = -3 is the y intercept.\r<BR>\n" );
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document.write( "Now let's try x = 1<BR>\n" );
document.write( "y = 2x-3<BR>\n" );
document.write( "y = 2*1-3<BR>\n" );
document.write( "y = 2-3<BR>\n" );
document.write( "y = -1<BR>\n" );
document.write( "This produces the ordered pair (1,-1)\r<BR>\n" );
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document.write( "Now let's try x = 2<BR>\n" );
document.write( "y = 2x-3<BR>\n" );
document.write( "y = 2*2-3<BR>\n" );
document.write( "y = 4-3<BR>\n" );
document.write( "y = 1<BR>\n" );
document.write( "This produces the ordered pair (2,1)\r<BR>\n" );
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document.write( "Repeat the process however many times you like.<BR>\n" );
document.write( "This is a small table of values<BR>\n" );
document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >x</TD><TD >y</TD></tr><tr><TD >0</TD><TD >-3</TD></tr><tr><TD >1</TD><TD >-1</TD></tr><tr><TD >2</TD><TD >1</TD></tr><tr><TD >3</TD><TD >3</TD></tr><tr><TD >4</TD><TD >5</TD></tr>\n" );
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document.write( "Each time x goes up by 1, y goes up by 2.<BR>\n" );
document.write( "This is exactly because the slope = 2 = 2/1.<BR>\n" );
document.write( "slope = rise/run = 2/1<BR>\n" );
document.write( "rise = 2 = go up 2<BR>\n" );
document.write( "run = 1 = go right 1\r<BR>\n" );
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document.write( "Graph<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-1%2C5%2C-5%2C7%2C%0D%0Agraph%28400%2C400%2C-1%2C5%2C-5%2C7%2C-100%2C2x-3%29%2C%0D%0A%0D%0Acircle%280%2C-3%2C0.05%29%2Ccircle%280%2C-3%2C0.07%29%2Ccircle%280%2C-3%2C0.09%29%2Ccircle%280%2C-3%2C0.11%29%2Ccircle%281%2C-1%2C0.05%29%2Ccircle%281%2C-1%2C0.07%29%2Ccircle%281%2C-1%2C0.09%29%2Ccircle%281%2C-1%2C0.11%29%2Ccircle%282%2C1%2C0.05%29%2Ccircle%282%2C1%2C0.07%29%2Ccircle%282%2C1%2C0.09%29%2Ccircle%282%2C1%2C0.11%29%2Ccircle%283%2C3%2C0.05%29%2Ccircle%283%2C3%2C0.07%29%2Ccircle%283%2C3%2C0.09%29%2Ccircle%283%2C3%2C0.11%29%2Ccircle%284%2C5%2C0.05%29%2Ccircle%284%2C5%2C0.07%29%2Ccircle%284%2C5%2C0.09%29%2Ccircle%284%2C5%2C0.11%29%2C%0D%0A%0D%0Alocate%280.1%2C-3.2%2Cmatrix%281%2C2%2C%22%280%2C%22%2C%22-3%29%22%29%29%2Clocate%281.1%2C-1.2%2Cmatrix%281%2C2%2C%22%281%2C%22%2C%22-1%29%22%29%29%2Clocate%282.1%2C0.8%2Cmatrix%281%2C2%2C%22%282%2C%22%2C%221%29%22%29%29%2Clocate%283.1%2C2.8%2Cmatrix%281%2C2%2C%22%283%2C%22%2C%223%29%22%29%29%2Clocate%284.1%2C4.8%2Cmatrix%281%2C2%2C%22%284%2C%22%2C%225%29%22%29%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Graph of -6x+3y=-9, aka y = 2x-3, through the following points<BR>\n" );
document.write( "(0, -3)<BR>\n" );
document.write( "(1, -1)<BR>\n" );
document.write( "(2, 1)<BR>\n" );
document.write( "(3, 3)<BR>\n" );
document.write( "(4, 5)\r<BR>\n" );
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document.write( "To find the x intercept, we plug in y = 0 to solve for x.<BR>\n" );
document.write( "y = 2x-3<BR>\n" );
document.write( "0 = 2x-3<BR>\n" );
document.write( "3 = 2x<BR>\n" );
document.write( "2x = 3<BR>\n" );
document.write( "x = 3/2<BR>\n" );
document.write( "x = 1.5<BR>\n" );
document.write( "The x intercept is located at (3/2, 0) aka (1.5, 0).<BR>\n" );
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